How to get adjacent vertices of a vertex? (with Python)
Yes, this is possible using BMEdge.other_vert

This script runs in edit-mode.

import bpy
import bmesh

obj = bpy.context.edit_object
me = obj.data
bm = bmesh.from_edit_mesh(me)

for v in bm.verts:
    for e in v.link_edges:
        v_other = e.other_vert(v)

        # print some info
        print("%d -&gt; %d via edge %d" % (v.index, v_other.index, e.index))